logit {poputils}

Logit and Inverse-Logit Functions

Description

Transform values to and from the logit scale. logit() calculates

Usage

logit(p)

invlogit(x)

Arguments

p

Values in the interval ⁠[0, 1]⁠. Can be an atomic vector, a matrix, or an rvec.

x

Values in the interval ⁠(-Inf, Inf)⁠. Can be an atomic vector, a matrix, or an rvec.

Details

x = \log \left(\frac{p}{1 - p}\right)

and invlogit() calculates

p = \frac{e^x}{1 + e^x}

To avoid overflow, invlogit() uses p = \frac{1}{1 + e^{-x}} internally for x where x > 0.

In some of the demographic literature, the logit function is defined as

x = \frac{1}{2} \log \left(\frac{p}{1 - p}\right).

logit() and invlogit() follow the conventions in statistics and machine learning, and omit the \frac{1}{2}.

Value

• A vector of doubles, if p or x is a vector.

• A matrix of doubles, if p or x is a matrix.

• An object of class rvec_dbl, if p or x is an rvec.

Examples

p <- c(0.5, 1, 0.2)
logit(p)
invlogit(logit(p))